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Math Help - Finding Average values

  1. #1
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    Finding Average values

    1. Find the average value of :
    on the interval

    Work: I know the formula is 1/(b - a) * ∫ f(x) dx (from x=a to b).

    so I got (1/ (13pi/6))

    Integrated 4sinx+7cosx= 4-cosx+7sinx, plugged in (13pi/6) and also 0 and subtracted them.

    ((13pi/6))[((4-cos((13pi/6))+7sin((13pi/6))))-((4-cos(0)+7sin(0)))]

    But that is wrong...

    2.find the average value of on the interval

    same as above, it is (1/1)* integral of cos^4xsinx [from 0 to 1]
    intregal of cos^4xsinx =(3+4cos(2x)+cos(4x))/8 -cosx

    (3+4cos(2)+cos(4))/8*-cos1-(3+4cos(0)+cos(0))/8*-cos0
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  2. #2
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    Quote Originally Posted by softballchick View Post
    1. Find the average value of :
    on the interval
    Note that \int {4\sin (x) + 7\cos (x) =  - 4\cos (x) + 7\sin (x)}
    Did you divide by \frac{13\pi}{6}~?
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  3. #3
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    thanks! Silly mistake, I multiplied it by 13pi/6 instead of 1/(13pi/6)
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